Chaotic Responses to Pulse-Train Stimulation in the Nagumo Neural Circuit

Yasutomo OHGUCHI  Yukio YANO  Kenzo MURAZUMI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E76-A   No.3   pp.459-466
Publication Date: 1993/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Phenomena and Analysis
chaos,  bifurcation,  neuron,  membrane,  Nagumo model,  BVP model,  Hodgkin-Huxley equations,  

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Responses in the Nagumo neural circuit to pulse-train stimulation are studied using the time sequence, phase diagram, Poincare section, return map, firing rate, Lyapunov number and bifurcation diagram. For the mono-stable neuron with an equilibrium point deeper than the maximal point of a tunnel diode curve, main responses are periodic or all-or-none and chaotic responses are rarely observed. For the neuron with an equilibrium point located near the maximal point, the response to one input pulse oscillates after the undershoot and responses to pulse-trains make complex bifurcation structure in the threshold diagram. The ranges of periodic responses are stratified in the diagram. There exist broad regions of chaotic responses and chaos is not a special response of the Nagumo circuit, but it often comes out. The results are different from those obtained from Hodgkin-Huxley equations and the BVP model.